Nokia Lumia 820 - What to do if sending of SMS messages doesn't work in my Lumia phone when using the international number format?

If the sending of the SMS messages doesn't succeed when using the international number format (+ country code), toggle the International assist option in Settings > Applications > Phone.

The International assist setting is turned on by default and can help to correct common dialing mistakes when making an international call. In some operator networks you may, however, need to turn this setting off to be able to send or reply to the SMS messages.